Algebra Examples

$(3 x + y) (x + y)$

Step 1

Expand $(3 x + y) (x + y)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 x (x + y) + y (x + y)$

Step 1.2

Apply the distributive property.

$3 x \cdot x + 3 x y + y (x + y)$

Step 1.3

Apply the distributive property.

$3 x \cdot x + 3 x y + y x + y \cdot y$

$3 x \cdot x + 3 x y + y x + y \cdot y$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.1.1

Move $x$ .

$3 (x \cdot x) + 3 x y + y x + y \cdot y$

Step 2.1.1.2

Multiply $x$ by $x$ .

$3 x^{2} + 3 x y + y x + y \cdot y$

$3 x^{2} + 3 x y + y x + y \cdot y$

Step 2.1.2

Multiply $y$ by $y$ .

$3 x^{2} + 3 x y + y x + y^{2}$

$3 x^{2} + 3 x y + y x + y^{2}$

Step 2.2

Add $3 x y$ and $y x$ .

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Step 2.2.1

Reorder $y$ and $x$ .

$3 x^{2} + 3 x y + x y + y^{2}$

Step 2.2.2

Add $3 x y$ and $x y$ .

$3 x^{2} + 4 x y + y^{2}$

$3 x^{2} + 4 x y + y^{2}$

$3 x^{2} + 4 x y + y^{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$